10 Software
Hausman[2007] Logic and Philosophy Chapter 7
In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,
6/14/07 10 Software
To start learning how to symbolize sentences using predicate logic.
Hausman[2007] Logic and Philosophy Chapter 7
There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.
There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.
7/31/08
The very first lesson that we have a right to demand that logic shall teach us is, how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. To know what we think, to be masters of our own meaning, will make a solid foundation for great and weighty thought. [CS Peirce, How to make our ideas clear]
6/24/07 10 Software
You now have to tools to appraise arguments to the level of detail offered by predicate logic.
Let us run through how these might be used with a long and difficult example.
Consider the argument
6/20/07 10Software
To understand how the various restrictions on the quantificational rules work to exclude certain kinds of invalid inferences
Bergmann[2004] The Logic Book Section 10.1
If a derivation contains a line of the form
n (∀<variable>)<scope> <any justification>
then a line of the form
<<scope>[<constant>/<variable>]> 'n ∀E'
12/26/05
11/9/2007 10Software
The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).
Let us start with an Interpretation
Interpretation 1
Universe= {a,b}
F={a}
10 Software
The Tutorial
Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.
11/3/07